PARIS, June 18 (Reuters) - Boeing has received strong interest in a potential new member of its best-selling 737 aircraft range, the planemaker's new commercial chief said on Sunday.

Boeing is expected to launch the 190-230 seat 737 MAX 10 with more seats and a modified landing gear at the opening of the Paris Airshow on Monday, adding a larger, new version to its narrowbody medium-haul family to plug a gap against Airbus.

"We are working very closely with a large number of customers, with offers on the table," Boeing Commercial Airplanes Chief Executive Kevin McAllister said in a briefing.

He dismissed concerns by some financiers about fragmentation of the Boeing 737 MAX family into what would now be five separate models, potentially making some harder to finance.

"There is significant demand for each model," he said.

Speaking before the world's largest air show at Le Bourget from June 19 to 25, McAllister offered a glimpse of new Boeing market forecasts due to be published on Tuesday.

The world will need 41,000 commercial jets over the next 20 years, he said, a 4 percent increase from last year's Boeing forecast. By comparison, Airbus last week forecast 34,899 jets over the same period, which was 6 percent above its own 2016 forecast. Boeing will unveil detailed figures on Tuesday.

SERVICES PUSH

Boeing is working to complete a three-year study on the potential for a so-called "mid-market" jet that would sit between the existing narrowbody and widebody categories. The company is working on a cost and business case for such a plane.

"I would like to do it as quickly as we can," McAllister said, but added: "I would rather take the time to do it right."

Airbus has dismissed the case for such an aircraft, saying its A321neo, which can seat up to 240 people in an all-economy layout, mostly fits the gap. Boeing says the potential market spans 200 to 270 seats and requires an all-new plane.

McAllister, a former General Electric executive who was appointed in November, said there was huge potential for new digital technologies in production and in providing aftermarket services. Such services, which are key to engine makers and are now working their way into aircraft manufacturing, will be part of the decisions on whether to launch the mid-market jet.

The Boeing official called for greater efficiency from suppliers including Spirit AeroSystems, which builds the fuselage of 737 jets and parts of the 787 Dreamliner.

Boeing is involved in pricing negotiations with its former subsidiary, formed in 2005 from the sale of its Wichita base.

"We are still negotiating with Spirit. I expect the same accountability from the supply chain as we place on ourselves," McAllister said.

Spirit said in May talks were taking longer than expected and that there was still a gap on 737 and 787..

On the 777 mini-jumbo, whose production is slowing before the transition to a new model due to enter service in 2020, McAllister said the plane was sold out for 2017 but the firm had "some holes to fill" in the order book in 2018 and 2019. (Editing by Edmund Blair)